I like #2 idea also.
Except not the screws, or nails, and use a veneer piece and not plywood, maybe even a thin piece of wood paneling.
I would try to match the veneer in size to fit as exactly as possible, think perfectionist.
Then with some wood glue, or Elmer's, just glue it down placing it into the drawer from the top side.
If you cut it good enough to fit snugly, I think that would do it.
Clean the excess oozed out glue with a wetted paper towel!
__________________
.....
Rusty
|